TSTP Solution File: SWC380+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SWC380+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 20:42:59 EDT 2023

% Result   : Theorem 0.45s 1.15s
% Output   : CNFRefutation 0.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   98 (  24 unt;   0 def)
%            Number of atoms       :  460 ( 123 equ)
%            Maximal formula atoms :   18 (   4 avg)
%            Number of connectives :  553 ( 191   ~; 180   |; 144   &)
%                                         (   4 <=>;  34  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-4 aty)
%            Number of functors    :   12 (  12 usr;   5 con; 0-2 aty)
%            Number of variables   :  233 (  20 sgn; 120   !;  57   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( memberP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(X2,cons(X1,X3)) = X0
                    & ssList(X3) )
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).

fof(f23,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => hd(cons(X1,X0)) = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax23) ).

fof(f28,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(nil,X0) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).

fof(f36,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ( memberP(app(X1,X2),X0)
              <=> ( memberP(X2,X0)
                  | memberP(X1,X0) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax36) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( ( neq(X3,nil)
                        | ~ neq(X1,nil) )
                      & ( ! [X5] :
                            ( ssItem(X5)
                           => ! [X6] :
                                ( ssList(X6)
                               => ( app(cons(X5,nil),X6) != X3
                                  | cons(X5,nil) != X2 ) ) )
                        | ? [X4] :
                            ( memberP(X1,X4)
                            & cons(X4,nil) = X0
                            & ssItem(X4) )
                        | ~ neq(X1,nil) ) )
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( ( neq(X3,nil)
                          | ~ neq(X1,nil) )
                        & ( ! [X5] :
                              ( ssItem(X5)
                             => ! [X6] :
                                  ( ssList(X6)
                                 => ( app(cons(X5,nil),X6) != X3
                                    | cons(X5,nil) != X2 ) ) )
                          | ? [X4] :
                              ( memberP(X1,X4)
                              & cons(X4,nil) = X0
                              & ssItem(X4) )
                          | ~ neq(X1,nil) ) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( ( neq(X3,nil)
                          | ~ neq(X1,nil) )
                        & ( ! [X4] :
                              ( ssItem(X4)
                             => ! [X5] :
                                  ( ssList(X5)
                                 => ( app(cons(X4,nil),X5) != X3
                                    | cons(X4,nil) != X2 ) ) )
                          | ? [X6] :
                              ( memberP(X1,X6)
                              & cons(X6,nil) = X0
                              & ssItem(X6) )
                          | ~ neq(X1,nil) ) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f100,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( memberP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(X2,cons(X1,X3)) = X0
                    & ssList(X3) )
                & ssList(X2) ) )
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f129,plain,
    ! [X0] :
      ( ! [X1] :
          ( hd(cons(X1,X0)) = X1
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f135,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f147,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( memberP(app(X1,X2),X0)
              <=> ( memberP(X2,X0)
                  | memberP(X1,X0) ) )
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f222,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( ? [X4] :
                          ( ? [X5] :
                              ( app(cons(X4,nil),X5) = X3
                              & cons(X4,nil) = X2
                              & ssList(X5) )
                          & ssItem(X4) )
                      & ! [X6] :
                          ( ~ memberP(X1,X6)
                          | cons(X6,nil) != X0
                          | ~ ssItem(X6) )
                      & neq(X1,nil) ) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f223,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( ? [X4] :
                          ( ? [X5] :
                              ( app(cons(X4,nil),X5) = X3
                              & cons(X4,nil) = X2
                              & ssList(X5) )
                          & ssItem(X4) )
                      & ! [X6] :
                          ( ~ memberP(X1,X6)
                          | cons(X6,nil) != X0
                          | ~ ssItem(X6) )
                      & neq(X1,nil) ) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f222]) ).

fof(f233,plain,
    ! [X3,X2,X1,X0] :
      ( ( ? [X4] :
            ( ? [X5] :
                ( app(cons(X4,nil),X5) = X3
                & cons(X4,nil) = X2
                & ssList(X5) )
            & ssItem(X4) )
        & ! [X6] :
            ( ~ memberP(X1,X6)
            | cons(X6,nil) != X0
            | ~ ssItem(X6) )
        & neq(X1,nil) )
      | ~ sP6(X3,X2,X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).

fof(f234,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | sP6(X3,X2,X1,X0) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(definition_folding,[],[f223,f233]) ).

fof(f239,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( memberP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(X2,cons(X1,X3)) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ? [X2] :
                  ( ? [X3] :
                      ( app(X2,cons(X1,X3)) = X0
                      & ssList(X3) )
                  & ssList(X2) )
              | ~ memberP(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f100]) ).

fof(f240,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( memberP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(X2,cons(X1,X3)) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ? [X4] :
                  ( ? [X5] :
                      ( app(X4,cons(X1,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              | ~ memberP(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f239]) ).

fof(f241,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( app(X4,cons(X1,X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( app(sK9(X0,X1),cons(X1,X5)) = X0
            & ssList(X5) )
        & ssList(sK9(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f242,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( app(sK9(X0,X1),cons(X1,X5)) = X0
          & ssList(X5) )
     => ( app(sK9(X0,X1),cons(X1,sK10(X0,X1))) = X0
        & ssList(sK10(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f243,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( memberP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(X2,cons(X1,X3)) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ( app(sK9(X0,X1),cons(X1,sK10(X0,X1))) = X0
                & ssList(sK10(X0,X1))
                & ssList(sK9(X0,X1)) )
              | ~ memberP(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f240,f242,f241]) ).

fof(f325,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( memberP(app(X1,X2),X0)
                  | ( ~ memberP(X2,X0)
                    & ~ memberP(X1,X0) ) )
                & ( memberP(X2,X0)
                  | memberP(X1,X0)
                  | ~ memberP(app(X1,X2),X0) ) )
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f147]) ).

fof(f326,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( memberP(app(X1,X2),X0)
                  | ( ~ memberP(X2,X0)
                    & ~ memberP(X1,X0) ) )
                & ( memberP(X2,X0)
                  | memberP(X1,X0)
                  | ~ memberP(app(X1,X2),X0) ) )
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f325]) ).

fof(f346,plain,
    ! [X3,X2,X1,X0] :
      ( ( ? [X4] :
            ( ? [X5] :
                ( app(cons(X4,nil),X5) = X3
                & cons(X4,nil) = X2
                & ssList(X5) )
            & ssItem(X4) )
        & ! [X6] :
            ( ~ memberP(X1,X6)
            | cons(X6,nil) != X0
            | ~ ssItem(X6) )
        & neq(X1,nil) )
      | ~ sP6(X3,X2,X1,X0) ),
    inference(nnf_transformation,[],[f233]) ).

fof(f347,plain,
    ! [X0,X1,X2,X3] :
      ( ( ? [X4] :
            ( ? [X5] :
                ( app(cons(X4,nil),X5) = X0
                & cons(X4,nil) = X1
                & ssList(X5) )
            & ssItem(X4) )
        & ! [X6] :
            ( ~ memberP(X2,X6)
            | cons(X6,nil) != X3
            | ~ ssItem(X6) )
        & neq(X2,nil) )
      | ~ sP6(X0,X1,X2,X3) ),
    inference(rectify,[],[f346]) ).

fof(f348,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( app(cons(X4,nil),X5) = X0
              & cons(X4,nil) = X1
              & ssList(X5) )
          & ssItem(X4) )
     => ( ? [X5] :
            ( app(cons(sK54(X0,X1),nil),X5) = X0
            & cons(sK54(X0,X1),nil) = X1
            & ssList(X5) )
        & ssItem(sK54(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f349,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( app(cons(sK54(X0,X1),nil),X5) = X0
          & cons(sK54(X0,X1),nil) = X1
          & ssList(X5) )
     => ( app(cons(sK54(X0,X1),nil),sK55(X0,X1)) = X0
        & cons(sK54(X0,X1),nil) = X1
        & ssList(sK55(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f350,plain,
    ! [X0,X1,X2,X3] :
      ( ( app(cons(sK54(X0,X1),nil),sK55(X0,X1)) = X0
        & cons(sK54(X0,X1),nil) = X1
        & ssList(sK55(X0,X1))
        & ssItem(sK54(X0,X1))
        & ! [X6] :
            ( ~ memberP(X2,X6)
            | cons(X6,nil) != X3
            | ~ ssItem(X6) )
        & neq(X2,nil) )
      | ~ sP6(X0,X1,X2,X3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK54,sK55])],[f347,f349,f348]) ).

fof(f351,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( ~ neq(X3,nil)
                        & neq(X1,nil) )
                      | sP6(X3,X2,X1,X0) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | sP6(X3,X2,X1,sK56) )
                  & sK56 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK56) ) ),
    introduced(choice_axiom,[]) ).

fof(f352,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( ~ neq(X3,nil)
                    & neq(X1,nil) )
                  | sP6(X3,X2,X1,sK56) )
                & sK56 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( ~ neq(X3,nil)
                  & neq(sK57,nil) )
                | sP6(X3,X2,sK57,sK56) )
              & sK56 = X2
              & sK57 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK57) ) ),
    introduced(choice_axiom,[]) ).

fof(f353,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( ~ neq(X3,nil)
                & neq(sK57,nil) )
              | sP6(X3,X2,sK57,sK56) )
            & sK56 = X2
            & sK57 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( ~ neq(X3,nil)
              & neq(sK57,nil) )
            | sP6(X3,sK58,sK57,sK56) )
          & sK56 = sK58
          & sK57 = X3
          & ssList(X3) )
      & ssList(sK58) ) ),
    introduced(choice_axiom,[]) ).

fof(f354,plain,
    ( ? [X3] :
        ( ( ( ~ neq(X3,nil)
            & neq(sK57,nil) )
          | sP6(X3,sK58,sK57,sK56) )
        & sK56 = sK58
        & sK57 = X3
        & ssList(X3) )
   => ( ( ( ~ neq(sK59,nil)
          & neq(sK57,nil) )
        | sP6(sK59,sK58,sK57,sK56) )
      & sK56 = sK58
      & sK57 = sK59
      & ssList(sK59) ) ),
    introduced(choice_axiom,[]) ).

fof(f355,plain,
    ( ( ( ~ neq(sK59,nil)
        & neq(sK57,nil) )
      | sP6(sK59,sK58,sK57,sK56) )
    & sK56 = sK58
    & sK57 = sK59
    & ssList(sK59)
    & ssList(sK58)
    & ssList(sK57)
    & ssList(sK56) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK56,sK57,sK58,sK59])],[f234,f354,f353,f352,f351]) ).

fof(f364,plain,
    ! [X2,X3,X0,X1] :
      ( memberP(X0,X1)
      | app(X2,cons(X1,X3)) != X0
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f243]) ).

fof(f448,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f457,plain,
    ! [X0,X1] :
      ( hd(cons(X1,X0)) = X1
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f129]) ).

fof(f462,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f135]) ).

fof(f473,plain,
    ! [X2,X0,X1] :
      ( memberP(app(X1,X2),X0)
      | ~ memberP(X1,X0)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f326]) ).

fof(f556,plain,
    ! [X2,X3,X0,X1,X6] :
      ( ~ memberP(X2,X6)
      | cons(X6,nil) != X3
      | ~ ssItem(X6)
      | ~ sP6(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f350]) ).

fof(f557,plain,
    ! [X2,X3,X0,X1] :
      ( ssItem(sK54(X0,X1))
      | ~ sP6(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f350]) ).

fof(f558,plain,
    ! [X2,X3,X0,X1] :
      ( ssList(sK55(X0,X1))
      | ~ sP6(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f350]) ).

fof(f559,plain,
    ! [X2,X3,X0,X1] :
      ( cons(sK54(X0,X1),nil) = X1
      | ~ sP6(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f350]) ).

fof(f560,plain,
    ! [X2,X3,X0,X1] :
      ( app(cons(sK54(X0,X1),nil),sK55(X0,X1)) = X0
      | ~ sP6(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f350]) ).

fof(f561,plain,
    ssList(sK56),
    inference(cnf_transformation,[],[f355]) ).

fof(f565,plain,
    sK57 = sK59,
    inference(cnf_transformation,[],[f355]) ).

fof(f566,plain,
    sK56 = sK58,
    inference(cnf_transformation,[],[f355]) ).

fof(f567,plain,
    ( neq(sK57,nil)
    | sP6(sK59,sK58,sK57,sK56) ),
    inference(cnf_transformation,[],[f355]) ).

fof(f568,plain,
    ( ~ neq(sK59,nil)
    | sP6(sK59,sK58,sK57,sK56) ),
    inference(cnf_transformation,[],[f355]) ).

fof(f569,plain,
    ( ~ neq(sK59,nil)
    | sP6(sK59,sK58,sK59,sK58) ),
    inference(definition_unfolding,[],[f568,f565,f566]) ).

fof(f570,plain,
    ( neq(sK59,nil)
    | sP6(sK59,sK58,sK59,sK58) ),
    inference(definition_unfolding,[],[f567,f565,f565,f566]) ).

fof(f572,plain,
    ssList(sK58),
    inference(definition_unfolding,[],[f561,f566]) ).

fof(f574,plain,
    ! [X2,X3,X1] :
      ( memberP(app(X2,cons(X1,X3)),X1)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssList(app(X2,cons(X1,X3))) ),
    inference(equality_resolution,[],[f364]) ).

fof(f600,plain,
    ! [X2,X0,X1,X6] :
      ( ~ memberP(X2,X6)
      | ~ ssItem(X6)
      | ~ sP6(X0,X1,X2,cons(X6,nil)) ),
    inference(equality_resolution,[],[f556]) ).

cnf(c_54,plain,
    ( ~ ssList(app(X0,cons(X1,X2)))
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2)
    | memberP(app(X0,cons(X1,X2)),X1) ),
    inference(cnf_transformation,[],[f574]) ).

cnf(c_141,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f448]) ).

cnf(c_150,plain,
    ( ~ ssItem(X0)
    | ~ ssList(X1)
    | hd(cons(X0,X1)) = X0 ),
    inference(cnf_transformation,[],[f457]) ).

cnf(c_155,plain,
    ( ~ ssList(X0)
    | app(nil,X0) = X0 ),
    inference(cnf_transformation,[],[f462]) ).

cnf(c_166,plain,
    ( ~ memberP(X0,X1)
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2)
    | memberP(app(X0,X2),X1) ),
    inference(cnf_transformation,[],[f473]) ).

cnf(c_246,plain,
    ( ~ sP6(X0,X1,X2,X3)
    | app(cons(sK54(X0,X1),nil),sK55(X0,X1)) = X0 ),
    inference(cnf_transformation,[],[f560]) ).

cnf(c_247,plain,
    ( ~ sP6(X0,X1,X2,X3)
    | cons(sK54(X0,X1),nil) = X1 ),
    inference(cnf_transformation,[],[f559]) ).

cnf(c_248,plain,
    ( ~ sP6(X0,X1,X2,X3)
    | ssList(sK55(X0,X1)) ),
    inference(cnf_transformation,[],[f558]) ).

cnf(c_249,plain,
    ( ~ sP6(X0,X1,X2,X3)
    | ssItem(sK54(X0,X1)) ),
    inference(cnf_transformation,[],[f557]) ).

cnf(c_250,plain,
    ( ~ sP6(X0,X1,X2,cons(X3,nil))
    | ~ memberP(X2,X3)
    | ~ ssItem(X3) ),
    inference(cnf_transformation,[],[f600]) ).

cnf(c_252,negated_conjecture,
    ( ~ neq(sK59,nil)
    | sP6(sK59,sK58,sK59,sK58) ),
    inference(cnf_transformation,[],[f569]) ).

cnf(c_253,negated_conjecture,
    ( sP6(sK59,sK58,sK59,sK58)
    | neq(sK59,nil) ),
    inference(cnf_transformation,[],[f570]) ).

cnf(c_257,negated_conjecture,
    ssList(sK58),
    inference(cnf_transformation,[],[f572]) ).

cnf(c_375,negated_conjecture,
    sP6(sK59,sK58,sK59,sK58),
    inference(global_subsumption_just,[status(thm)],[c_253,c_253,c_252]) ).

cnf(c_377,negated_conjecture,
    sP6(sK59,sK58,sK59,sK58),
    inference(global_subsumption_just,[status(thm)],[c_252,c_375]) ).

cnf(c_3139,plain,
    ( X0 != sK59
    | X1 != sK58
    | X2 != sK59
    | X3 != sK58
    | ssItem(sK54(X0,X1)) ),
    inference(resolution_lifted,[status(thm)],[c_249,c_377]) ).

cnf(c_3140,plain,
    ssItem(sK54(sK59,sK58)),
    inference(unflattening,[status(thm)],[c_3139]) ).

cnf(c_3144,plain,
    ( X0 != sK59
    | X1 != sK58
    | X2 != sK59
    | X3 != sK58
    | ssList(sK55(X0,X1)) ),
    inference(resolution_lifted,[status(thm)],[c_248,c_377]) ).

cnf(c_3145,plain,
    ssList(sK55(sK59,sK58)),
    inference(unflattening,[status(thm)],[c_3144]) ).

cnf(c_3149,plain,
    ( X0 != sK59
    | X1 != sK58
    | X2 != sK59
    | X3 != sK58
    | cons(sK54(X0,X1),nil) = X1 ),
    inference(resolution_lifted,[status(thm)],[c_247,c_377]) ).

cnf(c_3150,plain,
    cons(sK54(sK59,sK58),nil) = sK58,
    inference(unflattening,[status(thm)],[c_3149]) ).

cnf(c_3154,plain,
    ( X0 != sK59
    | X1 != sK58
    | X2 != sK59
    | X3 != sK58
    | app(cons(sK54(X0,X1),nil),sK55(X0,X1)) = X0 ),
    inference(resolution_lifted,[status(thm)],[c_246,c_377]) ).

cnf(c_3155,plain,
    app(cons(sK54(sK59,sK58),nil),sK55(sK59,sK58)) = sK59,
    inference(unflattening,[status(thm)],[c_3154]) ).

cnf(c_3159,plain,
    ( cons(X0,nil) != sK58
    | X1 != sK59
    | X2 != sK58
    | X3 != sK59
    | ~ memberP(X3,X0)
    | ~ ssItem(X0) ),
    inference(resolution_lifted,[status(thm)],[c_250,c_377]) ).

cnf(c_3160,plain,
    ( cons(X0,nil) != sK58
    | ~ memberP(sK59,X0)
    | ~ ssItem(X0) ),
    inference(unflattening,[status(thm)],[c_3159]) ).

cnf(c_6511,plain,
    app(sK58,sK55(sK59,sK58)) = sK59,
    inference(light_normalisation,[status(thm)],[c_3155,c_3150]) ).

cnf(c_11758,plain,
    ( ~ memberP(sK59,sK54(sK59,sK58))
    | ~ ssItem(sK54(sK59,sK58)) ),
    inference(superposition,[status(thm)],[c_3150,c_3160]) ).

cnf(c_11759,plain,
    ~ memberP(sK59,sK54(sK59,sK58)),
    inference(forward_subsumption_resolution,[status(thm)],[c_11758,c_3140]) ).

cnf(c_11987,plain,
    ( ~ ssList(app(X0,cons(sK54(sK59,sK58),nil)))
    | ~ ssItem(sK54(sK59,sK58))
    | ~ ssList(X0)
    | ~ ssList(nil)
    | memberP(app(X0,sK58),sK54(sK59,sK58)) ),
    inference(superposition,[status(thm)],[c_3150,c_54]) ).

cnf(c_11988,plain,
    ( ~ ssList(app(X0,sK58))
    | ~ ssItem(sK54(sK59,sK58))
    | ~ ssList(X0)
    | ~ ssList(nil)
    | memberP(app(X0,sK58),sK54(sK59,sK58)) ),
    inference(light_normalisation,[status(thm)],[c_11987,c_3150]) ).

cnf(c_11989,plain,
    ( ~ ssList(app(X0,sK58))
    | ~ ssList(X0)
    | memberP(app(X0,sK58),sK54(sK59,sK58)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11988,c_141,c_3140]) ).

cnf(c_12086,plain,
    app(nil,sK58) = sK58,
    inference(superposition,[status(thm)],[c_257,c_155]) ).

cnf(c_12139,plain,
    ( ~ ssList(app(nil,sK58))
    | ~ ssList(nil)
    | memberP(sK58,sK54(sK59,sK58)) ),
    inference(superposition,[status(thm)],[c_12086,c_11989]) ).

cnf(c_12140,plain,
    ( ~ ssList(nil)
    | ~ ssList(sK58)
    | memberP(sK58,sK54(sK59,sK58)) ),
    inference(light_normalisation,[status(thm)],[c_12139,c_12086]) ).

cnf(c_12141,plain,
    memberP(sK58,sK54(sK59,sK58)),
    inference(forward_subsumption_resolution,[status(thm)],[c_12140,c_257,c_141]) ).

cnf(c_13100,plain,
    ( ~ ssList(X0)
    | hd(cons(sK54(sK59,sK58),X0)) = sK54(sK59,sK58) ),
    inference(superposition,[status(thm)],[c_3140,c_150]) ).

cnf(c_13247,plain,
    hd(cons(sK54(sK59,sK58),nil)) = sK54(sK59,sK58),
    inference(superposition,[status(thm)],[c_141,c_13100]) ).

cnf(c_13254,plain,
    sK54(sK59,sK58) = hd(sK58),
    inference(light_normalisation,[status(thm)],[c_13247,c_3150]) ).

cnf(c_13346,plain,
    memberP(sK58,hd(sK58)),
    inference(demodulation,[status(thm)],[c_12141,c_13254]) ).

cnf(c_13348,plain,
    ~ memberP(sK59,hd(sK58)),
    inference(demodulation,[status(thm)],[c_11759,c_13254]) ).

cnf(c_13350,plain,
    ssItem(hd(sK58)),
    inference(demodulation,[status(thm)],[c_3140,c_13254]) ).

cnf(c_16922,plain,
    ( ~ ssList(sK55(sK59,sK58))
    | ~ memberP(sK58,X0)
    | ~ ssItem(X0)
    | ~ ssList(sK58)
    | memberP(sK59,X0) ),
    inference(superposition,[status(thm)],[c_6511,c_166]) ).

cnf(c_16956,plain,
    ( ~ memberP(sK58,X0)
    | ~ ssItem(X0)
    | memberP(sK59,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_16922,c_257,c_3145]) ).

cnf(c_17492,plain,
    ( ~ ssItem(hd(sK58))
    | memberP(sK59,hd(sK58)) ),
    inference(superposition,[status(thm)],[c_13346,c_16956]) ).

cnf(c_17493,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_17492,c_13348,c_13350]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWC380+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.12  % Command  : run_iprover %s %d THM
% 0.12/0.33  % Computer : n013.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Mon Aug 28 15:03:02 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.19/0.46  Running first-order theorem proving
% 0.19/0.46  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.45/1.15  % SZS status Started for theBenchmark.p
% 0.45/1.15  % SZS status Theorem for theBenchmark.p
% 0.45/1.15  
% 0.45/1.15  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.45/1.15  
% 0.45/1.15  ------  iProver source info
% 0.45/1.15  
% 0.45/1.15  git: date: 2023-05-31 18:12:56 +0000
% 0.45/1.15  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.45/1.15  git: non_committed_changes: false
% 0.45/1.15  git: last_make_outside_of_git: false
% 0.45/1.15  
% 0.45/1.15  ------ Parsing...
% 0.45/1.15  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.45/1.15  
% 0.45/1.15  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e  sup_sim: 1  sf_s  rm: 6 0s  sf_e  pe_s  pe_e 
% 0.45/1.15  
% 0.45/1.15  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 0.45/1.15  
% 0.45/1.15  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 0.45/1.15  ------ Proving...
% 0.45/1.15  ------ Problem Properties 
% 0.45/1.15  
% 0.45/1.15  
% 0.45/1.15  clauses                                 188
% 0.45/1.15  conjectures                             2
% 0.45/1.15  EPR                                     52
% 0.45/1.15  Horn                                    120
% 0.45/1.15  unary                                   23
% 0.45/1.15  binary                                  40
% 0.45/1.15  lits                                    628
% 0.45/1.15  lits eq                                 82
% 0.45/1.15  fd_pure                                 0
% 0.45/1.15  fd_pseudo                               0
% 0.45/1.15  fd_cond                                 21
% 0.45/1.15  fd_pseudo_cond                          14
% 0.45/1.15  AC symbols                              0
% 0.45/1.15  
% 0.45/1.15  ------ Schedule dynamic 5 is on 
% 0.45/1.15  
% 0.45/1.15  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.45/1.15  
% 0.45/1.15  
% 0.45/1.15  ------ 
% 0.45/1.15  Current options:
% 0.45/1.15  ------ 
% 0.45/1.15  
% 0.45/1.15  
% 0.45/1.15  
% 0.45/1.15  
% 0.45/1.15  ------ Proving...
% 0.45/1.15  
% 0.45/1.15  
% 0.45/1.15  % SZS status Theorem for theBenchmark.p
% 0.45/1.15  
% 0.45/1.15  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.45/1.15  
% 0.45/1.15  
%------------------------------------------------------------------------------